We report observations of HD 80606 using the 10.4-m Gran Telescopio Canarias ( GTC ) and the OSIRIS tunable filter imager . We acquired very-high-precision , narrow-band photometry in four bandpasses around the K i absorption feature during the January 2010 transit of HD 80606b and during out-of-transit observations conducted in January and April of 2010 . We obtained differential photometric precisions of \sim 2.08 \times 10 ^ { -4 } for the in-transit flux ratio measured at 769.91-nm , which probes the K i line core . We find no significant difference in the in-transit flux ratio between observations at 768.76 and 769.91 nm . Yet , we find a difference of \sim 8.09 \pm 2.88 \times 10 ^ { -4 } between these observations and observations at a longer wavelength that probes the K i wing ( 777.36 nm ) . While the presence of red noise in the transit data has a non-negligible effect on the uncertainties in the flux ratio , the 777.36-769.91 nm colour during transit shows no effects from red noise and also indicates a significant colour change , with a mean value of \sim 8.99 \pm 0.62 \times 10 ^ { -4 } . This large change in the colour is equivalent to a \sim 4.2 % change in the apparent planetary radius with wavelength , which is much larger than the atmospheric scale height . This implies the observations probed the atmosphere at very low pressures as well as a dramatic change in the pressure at which the slant optical depth reaches unity between \sim 770 and 777 nm . We hypothesize that the excess absorption may be due to K i in a high-speed wind being driven from the exoplanet ’ s exosphere . We discuss the viability of this and alternative interpretations , including stellar limb darkening , starspots , and effects from Earth ’ s atmosphere . We strongly encourage follow-up observations of HD 80606b to confirm the signal measured here . Finally , we discuss the future prospects for exoplanet characterization using tunable filter spectrophotometry .